Different nanostructures of boron nitride have been observed experimentally such as fullerenes, tubes, cones, and graphene. They have received much attention due to their physical, chemical, and electronic properties that lead them to numerous applications in many nanoscale devices. Joining between nanostructures gives rise to new structures with outstanding properties and potential applications for the design of probes for scanning tunneling microscopy and other nanoscale devices, as carriers for drug delivery and liquid separation. This paper utilizes calculus of variations to model the joining between two types of BN nanostructures, namely, BN nanotubes and BN nanocones. Based on the curvature of the join curve, the joining of these structures can be divided into two models. Model I refers to when the join profile includes positive curvature only, and Model II contains both positive and negative curvatures. The main goal here is to formulate the basic underlying structure from which any such small perturbations can be viewed as departures from an ideal model. For this scenario of joining, we successfully present simple models based on joining BN nanotubes to BN nanocones with five different angles of the cone.

中文翻译：

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氮化硼纳米锥和纳米管之间的连接

实验上已经观察到氮化硼的不同纳米结构，例如富勒烯，管，锥和石墨烯。由于它们的物理，化学和电子特性，它们在许多纳米级设备中得到了广泛的应用，因此受到了广泛的关注。纳米结构之间的结合产生了具有出色性能的新结构，并将其设计用于扫描隧道显微镜和其他纳米级设备的探针设计，作为药物输送和液体分离的载体。本文利用变化演算来模拟两种类型的BN纳米结构之间的连接，即BN纳米管和BN纳米锥。根据连接曲线的曲率，可以将这些结构的连接分为两个模型。模型I指的是连接轮廓仅包含正曲率，模型II包含正曲率和负曲率。这里的主要目标是制定基本的基础结构，从中可以将任何这种小扰动视为偏离理想模型的基础。对于这种连接方案，我们成功地提出了基于将BN纳米管连接到具有五个不同锥角的BN纳米锥的简单模型。